Nonlinear fractional distributed Halanay inequality and application to neural network systems

Mohammed D. Kassim and Nasser-eddine Tatar

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

Abstract: The standard first order distributed Halanay inequality is generalized in more than one direction. We prove a fractional nonlinear version of this inequality for a large class of kernels which are not necessarily exponentially decaying to zero. This result is used to prove Mittag-Leffler stability of a Hopfiled neural network system with not necessarily globally Lipschitz continuous activation functions. Two classes of important admissible kernels and an example are provided to illustrate our findings.

Keywords: Hopfield neural network; Mittag-Leffler stability; Caputo fractional derivative; Fractional Halanay inequality (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004847

DOI: 10.1016/j.chaos.2021.111130

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